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Where applicable reference has been made to Adams's List of Publications (A.2)

Items C. 1 - C.344 consist of lectures etc as part of Adams' role in teaching, C.345 - C.646 are from conferences and seminars he attended and C.647 - C.708 consist of lectures by others.

The material is principally Adams's undated ms drafts, notes and calculations documenting his research from the 1950s until his death. It was found in Adams's own folders with titles inscribed thereon.

These titles have been reproduced in the catalogue entries and form the basis for the arrangement of the material in an alphabetical sequence. At the end of this sequence is miscellaneous research material including 'work done' and 'work in progress'. The contents of bulky folders have been subdivided for ease of reference.

The collection is particularly noteworthy for its coverage of Adams's lectures, research and incoming correspondence.
Section A, Biographical, is not substantial. It includes a little material of Adams's relating to his own career including three Bedford School notebooks and his PhD thesis, and material assembled by I M James during the preparation of his Royal Society memoir.
Section B, Research, provides extensive documentation of Adams's research from the 1950s until his death. It is presented in an alphabetical sequence arranged by subject title.
Section C, Lectures, is the largest in the collection. Two subsections comprise Adams's lecture notes and other teaching material for courses given at Manchester and Cambridge, and material from conferences and seminars attended by Adams throughout the world including drafts of Adams's contributions and notes of contributions by others. A third subsection consists of Adams's ms notes found in filing cabinet drawers labelled 'Other people's lectures'. It includes notes taken by Adams as an undergraduate at Cambridge in 1949.
Section D, Publications, is very slight. It includes drafts of a few of Adams's scientific papers.
Section E, Correspondence, contains virtually no extended exchanges of correspondence as very few copies of Adams's own letters survive. There is, however, significant correspondence from colleagues such as M F (later Sir Michael) Atiyah, M G Barratt, P J Hilton, I M James and S MacLane, sometimes extending over a period of twenty or thirty years.

Lecture notes for course of eight summer-term lectures. Some sheets marked 'OLD'.

'Obstr [uctio]ns: Homotopy Groups'. Some material on back of duplicated typescript sheets 1954. At B.100 is rough draft of letter to G W Whitehead.

The correspondence chiefly relates to work towards two 1988 joint publications by Adams, Jackowski, J-P Haeberly and J P May 'A generalisation of the Segal conjecture' (Bibliog.no.78) and 'A generalisation of the Atiyah-Segal completion theorem'

Questionnaires on Adams's geometry lectures completed by students 1982; letter from student requesting 'a lecture on lie groups' 25 April 1985, with ms notes on lie groups.

The correspondence chiefly relates to work towards two 1988 joint publications by Adams, Jackowski, J-P Haeberly and J P May 'A generalisation of the Segal conjecture' (Bibliog.no.78) and 'A generalisation of the Atiyah-Segal completion theorem'

'Geometry hand-outs'.

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'Some applications of K-theory to homotopy theory', ms notes and tables.

Lecture notes.

'Killing htpy groups: stable case'.

'Killing htpy groups: unstable case'.

Questionnaires on content and style of Adams's IB geometry lectures completed by students 1974.

'Calculations using method of "killing htpy groups"...'.

'IB Geometry' example sheets; correspondence from D W Babbage re geometry examination questions 1974-75.